Identifying Latent Stochastic Differential Equations
This method addresses the challenge of modeling complex time series data for applications like video processing, but it appears incremental as it builds on existing frameworks like variational autoencoders and identifiability results.
The authors tackled the problem of learning latent stochastic differential equations (SDEs) from high-dimensional time series data, using a self-supervised variational autoencoder approach to recover SDE coefficients and latent variables up to an isometry in the infinite data limit, validated on simulated and real-world datasets.
We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown Itô process, the proposed method learns the mapping from ambient to latent space, and the underlying SDE coefficients, through a self-supervised learning approach. Using the framework of variational autoencoders, we consider a conditional generative model for the data based on the Euler-Maruyama approximation of SDE solutions. Furthermore, we use recent results on identifiability of latent variable models to show that the proposed model can recover not only the underlying SDE coefficients, but also the original latent variables, up to an isometry, in the limit of infinite data. We validate the method through several simulated video processing tasks, where the underlying SDE is known, and through real world datasets.